Ultimately, I want to change fci-rule-color based on the current theme's background color. So, when I change from a light theme to a dark theme, fci-rule-color remains a subtle shade off of the background color.

Since after collecting karma points one gets some mod's privileges, I can see you wanted to edit lawlist's answer. Why not post it as a separate answer instead of editing the existing one?
– wvxvwOct 8 '16 at 14:34

I didn't know it was a better option. I've moved my edits to a separate answer.
– JoeOct 9 '16 at 17:53

After a little bit more experimentation, this doesn't work for buffers that aren't visible when the code is run. I fell back to the turn-on, turn-off hack.
– JoeOct 6 '16 at 5:36

In addition to the window-list, you can loop through all buffers and operate on the ones where fci-mode is active. You would need to look at fci-upate-all-windows to see what makes it tick. You may wish to consider posting an alternative answer, or edit your question to contain a custom solution (e.g., underneath the question), rather than substantially modifying my own answer. My schedule is booked today and tomorrow, but if you need additional help, just let me know and I'll be able to lend a hand over the next few days as time permits.
– lawlistOct 6 '16 at 15:33

Thank you for the tip. I made an alternate answer so the proposed edit can get rejected.
– JoeOct 9 '16 at 17:54